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3 years ago

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What is the correct classification of the system of equations below? 5x + 6y = 1 y = -5x + 6 A. parallel B. coincident C. inters

ecting

1 answer:

babymother [125]3 years ago

7 0

Answer: OPTION C.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the system of equations:

$\left \{ {{5x + 6y = 1} \atop {y = -5x + 6}} \right.$

Solve for "y" from the first equation in order to write it in Slope-Intercept form:

$5x + 6y = 1\\\\6y=-5x+1\\\\y=-\frac{5}{6}x+\frac{1}{6}$

Since the lines have different slopes, they cannot be parallel or coincident. Therefore, they are Intersecting.

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Step-by-step explanation:

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3 years ago

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3 years ago

What is the ratio 15 inches to 6 feet as a fraction in simplest form?

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4 years ago

A software store has put some of its inventory on sale. Games are marked down by 15%, and security programs are marked down by 1

Katyanochek1 [597]

Answer:

Option D. $\$11.34$

Step-by-step explanation:

Let

x -----> the original price of one game

y ----> the original price of one security programs

Remember that

$100\%-15\%=85\%=85\100=0.85$

$100\%-18\%=82\%=82\100=0.82$

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we have that

$0.85(2x)=35.70\\1.70x=35.70\\x=\$21$

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Find the total pay without discount

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5 0

3 years ago

Read 2 more answers

Find the general solution of the diﬀerential equation y^(5) −2y^(4) + y^(3) = 0.

Gwar [14]

$y^{(5)}-2y^{(4)}+y^{(3)}=0$

We can reduce the order of the ODE by substituting $v(x)=y^{(3)}(x)$ , so that $v'(x)=y^{(4)}(x)$ and $v''(x)=y^{(5)}(x)$ . Then

$v''-2v'+v=0$

has characteristic equation

$r^2-2r+1=(r-1)^2=0$

with root $r=1$ , which has multiplicity 2, so that the characteristic solution is

$v_c=C_1e^x+C_2xe^x$

Integrate both sides to solve for $y''(x)$ :

$y''=C_1e^x+C_2e^x(x-1)+C_3$

$y''=C_1e^x+C_2xe^x+C_3$

Integrate again to solve for $y'(x)$ :

$y'=C_1e^x+C_2e^x(x-1)+C_3x+C_4$

$y'=C_1e^x+C_2xe^x+C_3x+C_4$

And one last time to solve for $y(x)$ :

$y=C_1e^x+C_2e^x(x-1)+\dfrac{C_3}2x^2+C_4x+C_5$

$\boxed{y(x)=C_1e^x+C_2e^x+C_3x^2+C_4x+C_5}$

6 0

3 years ago